A circle has a circumference of $6\pi$. It has an arc of length $\dfrac{58}{15}\pi$. What is the central angle of the arc, in degrees? ${6\pi}$ ${232^\circ}$ $\color{#DF0030}{\dfrac{58}{15}\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{s}{c}$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{58}{15}\pi \div 6\pi$ $\dfrac{\theta}{360 ^ \circ} = \dfrac{29}{45}$ $\theta = \dfrac{29}{45} \times 360 ^ \circ$ $\theta = 232^\circ$